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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">R</font>, <font color="Olive" title="b2">S</font> being  <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>  st <font color="Olive" title="b1">R</font> is <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> &amp; <font color="Olive" title="b2">S</font> is <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> &amp; <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Olive" title="b1">R</font> &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Olive" title="b2">S</font> &amp; <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Olive" title="b2">S</font> &amp; <font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a>  &amp; <font color="Olive" title="b1">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Olive" title="b2">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a>  holds <br/>( <font color="Olive" title="b2">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">S</font> )</span><br/><b>let </b><font color="Maroon" title="c4">R</font>, <font color="Maroon" title="c5">S</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">R</font> is <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> &amp; <font color="Maroon" title="c5">S</font> is <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> &amp; <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c4">R</font> &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c5">S</font> &amp; <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c5">S</font> &amp; <font color="Maroon" title="c4">R</font>,<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a>  &amp; <font color="Maroon" title="c4">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a>  implies ( <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">S</font> ) )</span><br/>









<b>assume </b><a NAME="E1:61"/><i><font color="Green" title="E57">A1</font></i>: 
( <font color="Maroon" title="c4">R</font> is <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> &amp; <font color="Maroon" title="c5">S</font> is <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> &amp; <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c4">R</font> &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c5">S</font> &amp; <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c5">S</font> &amp; <font color="Maroon" title="c4">R</font>,<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a>  &amp; <font color="Maroon" title="c4">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">S</font> )</span><br/>

<b>set </b><font color="Maroon" title="c6">P</font> = <font color="Maroon" title="c4">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c7">Q</font> = <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c8">T</font> = <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c9">F1</font> =  <a href="wellord1.html#K3" title="WELLORD1:func.3">canonical_isomorphism_of</a> <font color="Maroon" title="c4">R</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>;<br/>
<a NAME="E2:61"/><i><font color="Green" title="E58">A2</font></i>: 
 <a href="wellord1.html#K3" title="WELLORD1:func.3">canonical_isomorphism_of</a> <font color="Maroon" title="c4">R</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="wellord1.html#R3" title="WELLORD1:pred.3">is_isomorphism_of</a> <font color="Maroon" title="c4">R</font>,<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span>
 
<b>by </b><i><a class="txt" href="wellord1.html#E1:61"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="wellord1.html#D9" target="_self" title="WELLORD1:def.9">Def9</a></i>;<br/>
<a NAME="E3:61"/>
<font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c4">R</font>
 
<b>by </b><i><a class="ref" href="wellord1.html#T13" target="_self" title="WELLORD1:th.13">Th13</a></i>;<br/>
<a NAME="E4:61"/><b>then </b><i><font color="Green" title="E59">A3</font></i>: 
<font color="Maroon" title="c4">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wellord1.html#K3" title="WELLORD1:func.3">canonical_isomorphism_of</a> <font color="Maroon" title="c4">R</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a> 
 
<b>by </b><i><a class="txt" href="wellord1.html#E1:61"><i><font color="Green" title="E57">A1</font></i></a>, <a class="txt" href="wellord1.html#E2:61"><i><font color="Green" title="E58">A2</font></i></a>, <a class="ref" href="wellord1.html#T59" target="_self" title="WELLORD1:th.59">Th59</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">d</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:61"/><i><font color="Green" title="E60">A4</font></i>: 
( <font color="Maroon" title="c10">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="wellord1.html#K3" title="WELLORD1:func.3">canonical_isomorphism_of</a> <font color="Maroon" title="c4">R</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c10">d</font> )
 <b>by </b><i><a class="txt" href="wellord1.html#E1:61"><i><font color="Green" title="E57">A1</font></i></a>, <a class="txt" href="wellord1.html#E2:61"><i><font color="Green" title="E58">A2</font></i></a>, <a class="ref" href="wellord1.html#T60" target="_self" title="WELLORD1:th.60">Th60</a></i>;<br/>
<a NAME="E7:61"/><i><font color="Green" title="E61">A5</font></i>: 
<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="wellord1.html#E1:61"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="wellord1.html#T40" target="_self" title="WELLORD1:th.40">Th40</a></i>;<br/>
<a NAME="E8:61"/><b>then </b><i><font color="Green" title="E62">A6</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c10">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c10">d</font>
 
<b>by </b><i><a class="txt" href="wellord1.html#E1:61"><i><font color="Green" title="E57">A1</font></i></a>, <a class="txt" href="wellord1.html#E6:61"><i><font color="Green" title="E60">A4</font></i></a>, <a class="ref" href="wellord1.html#T35" target="_self" title="WELLORD1:th.35">Th35</a></i>;<br/>
<a NAME="E9:61"/>
<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font></span>)</span>,<font color="Maroon" title="c4">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a> 
 
<b>by </b><i><a class="txt" href="wellord1.html#E1:61"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="wellord1.html#T50" target="_self" title="WELLORD1:th.50">Th50</a></i>;<br/>
<a NAME="E10:61"/><b>then </b><i><font color="Green" title="E63">A7</font></i>: 
<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c10">d</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a> 
 
<b>by </b><i><a class="txt" href="wellord1.html#E4:61"><i><font color="Green" title="E59">A3</font></i></a>, <a class="txt" href="wellord1.html#E6:61"><i><font color="Green" title="E60">A4</font></i></a>, <a class="ref" href="wellord1.html#T52" target="_self" title="WELLORD1:th.52">Th52</a></i>;<br/>
<a NAME="E11:61"/><i><font color="Green" title="E64">A8</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="wellord1.html#K3" title="WELLORD1:func.3">canonical_isomorphism_of</a> <font color="Maroon" title="c4">R</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font>
 
<b>by </b><i><a class="txt" href="wellord1.html#E2:61"><i><font color="Green" title="E58">A2</font></i></a>, <a class="txt" href="wellord1.html#E7:61"><i><font color="Green" title="E61">A5</font></i></a>, <a class="ref" href="wellord1.html#D7" target="_self" title="WELLORD1:def.7">Def7</a></i>;<br/>
<a NAME="E12:61"/><b>then </b><i><font color="Green" title="E65">A9</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c10">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font>
 
<b>by </b><i><a class="txt" href="wellord1.html#E6:61"><i><font color="Green" title="E60">A4</font></i></a>, <a class="ref" href="relat_1.html#T144" title="RELAT_1:th.144">RELAT_1:144</a></i>;<br/>
<a NAME="E13:61"/><i><font color="Green" title="E66">A10</font></i>: 
<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font></span>)</span>,<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c10">d</font></span>)</span> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a> 
 
<b>by </b><i><a class="txt" href="wellord1.html#E6:61"><i><font color="Green" title="E60">A4</font></i></a>, <a class="txt" href="wellord1.html#E8:61"><i><font color="Green" title="E62">A6</font></i></a>, <a class="txt" href="wellord1.html#E10:61"><i><font color="Green" title="E63">A7</font></i></a>, <a class="txt" href="wellord1.html#E11:61"><i><font color="Green" title="E64">A8</font></i></a>, <a class="ref" href="wellord1.html#T29" target="_self" title="WELLORD1:th.29">Th29</a>, <a class="ref" href="relat_1.html#T144" title="RELAT_1:th.144">RELAT_1:144</a></i>;<br/>
<a NAME="E14:61"/>
<font color="Maroon" title="c10">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c5">S</font>
 
<b>by </b><i><a class="txt" href="wellord1.html#E6:61"><i><font color="Green" title="E60">A4</font></i></a>, <a class="ref" href="wellord1.html#T19" target="_self" title="WELLORD1:th.19">Th19</a></i>;<br/>
<b>hence </b><a NAME="E15:61"/>
<font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c3">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">S</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">b</font>
 <b>by </b><i><a class="txt" href="wellord1.html#E1:61"><i><font color="Green" title="E57">A1</font></i></a>, <a class="txt" href="wellord1.html#E8:61"><i><font color="Green" title="E62">A6</font></i></a>, <a class="txt" href="wellord1.html#E12:61"><i><font color="Green" title="E65">A9</font></i></a>, <a class="txt" href="wellord1.html#E13:61"><i><font color="Green" title="E66">A10</font></i></a>, <a class="ref" href="wellord1.html#T58" target="_self" title="WELLORD1:th.58">Th58</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">S</font></span><br/>

<b>hence </b><a NAME="E16:61"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">S</font>
 <b>by </b><i><a class="txt" href="wellord1.html#E1:61"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="wellord1.html#T37" target="_self" title="WELLORD1:th.37">Th37</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
